The move, which has been confirmed by CNBC, could be a sign that Flynn, Trump's former national security advisor, is cooperating — or negotiating an agreement — with Mueller. The former FBI director's probe is investigating the Trump campaign, Russian meddling in the U.S. election last year and other related concerns.

The Times reported that the president's attorneys believe Flynn "has, at the least, begun discussions" with Mueller's investigators regarding possible cooperation.

Jay Sekulow, an attorney for the president, told CNBC he wasn't surprised by Flynn's decision. Such a move is a typical when a plea is being discussed, Sekulow said. An attorney for Flynn did not immediately respond to a request for comment from CNBC.

"Assuming that the story is true, cooperation is the most likely explanation," Sol Wisenberg, former deputy independent counsel under Kenneth Starr, told CNBC.

Flynn was an important advisor to the Trump campaign and served briefly as national security advisor in the Trump White House. He resigned after only 24 days in the administration following reports that he had misled Vice President Mike Pence regarding conversations he had with top Russian officials.

The fact that Flynn's attorneys have stopped cooperating with Trump's team does not necessarily mean that Flynn is cooperating with prosecutors. The Times wrote: "Some lawyers withdraw from information-sharing arrangements as soon as they begin negotiating with prosecutors. And such negotiations sometimes fall apart."

In March, Flynn's attorney released a statement saying that "General Flynn certainly has a story to tell, and he very much wants to tell it, should the circumstances permit."

The president tweeted at the time that Flynn "should ask for immunity," arguing that investigations into his former advisor were a "witch hunt."